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Does anyone know an explicit uniformizer for $\mathbf{Q}_p(\zeta_{p^n}, p^{\frac{1}{p^n}}) / \mathbf{Q}_p$? I was reading the question "http"https://mathoverflow.net/questions/12463/adding-an-n-th-root-to-q-p" where dke mentions this question but it remains unanswered and I would like to use this for some calculations.

Does anyone know an explicit uniformizer for $\mathbf{Q}_p(\zeta_{p^n}, p^{\frac{1}{p^n}}) / \mathbf{Q}_p$? I was reading the question "http://mathoverflow.net/questions/12463/adding-an-n-th-root-to-q-p" where dke mentions this question but it remains unanswered and I would like to use this for some calculations.

Does anyone know an explicit uniformizer for $\mathbf{Q}_p(\zeta_{p^n}, p^{\frac{1}{p^n}}) / \mathbf{Q}_p$? I was reading the question "https://mathoverflow.net/questions/12463/adding-an-n-th-root-to-q-p" where dke mentions this question but it remains unanswered and I would like to use this for some calculations.

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Uniformizer for splitting field of p^{1/p^n} over p-adics

Does anyone know an explicit uniformizer for $\mathbf{Q}_p(\zeta_{p^n}, p^{\frac{1}{p^n}}) / \mathbf{Q}_p$? I was reading the question "http://mathoverflow.net/questions/12463/adding-an-n-th-root-to-q-p" where dke mentions this question but it remains unanswered and I would like to use this for some calculations.